It is strange, because the likelihood of rain is above what, in my opinion, suits a 2nd conditional.

'If it rains, I cannot come.' is not strange at all. Even with the most accurate weather forecast, the 2nd conditional is for unlikely situations, e.g. 'If I was president, ...', 'If I had three legs, ...'.

The 3rd conditional then is for conditional sentences that happened already and thus there is no way of the following sentence to be true. Again, you can use could or might as well as would.

If I had had more time, I could have fixed it.If I had had less time, I couldn't have fixed it. (But fortunately, I could.)

We can not learn english without using grammer. Some predefined words have been provided to use english language. These word must be used in correct situation. Especially some words like may,might be....etc.Could is also used like this. This word can tells the capacity of the one person. It can also used for showing the politeness and also used in past tense and could't gives the negative meaning.=======================cadeburtonJob Opportunities

well,in my opinion,maybe this is better "If it rained, I couldn't have come to your house."just as "negrita" wrote "If I hadn't taken the job in New York, I wouldn't have met the President."and "marcchehab" wrote "If I had had more time, I could have fixed it.If I had had less time, I couldn't have fixed it."they are all virtual sentences